Nonlocal games and quantum permutation groups

We present a strong connection between quantum information and the theory of quantum permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs based on quantum automorphisms from the theory of quantum groups, and then show that this is equivalent to the previously defined notion of quantum isomorphism corresponding to perfect quantum strategies to the isomorphism game. Moreover, we show that two connected graphs X and Y are quantum isomorphic if and only if there exists x is an element of V(X) and y is an element of V(Y) that are in the same orbit of the quantum automorphism group of the disjoint union of X and Y. This connection links quantum groups to the more concrete notion of nonlocal games and physically observable quantum behaviours. In this work, we exploit this by using ideas and results from quantum information in order to prove new results about quantum automorphism groups of graphs, and about quantum permutation groups more generally. In particular, we show that asymptotically almost surely all graphs have trivial quantum automorphism group. Furthermore, we use examples of quantum isomorphic graphs from previous work to construct an infinite family of graphs which are quantum vertex transitive but fail to be vertex transitive, answering a question from the quantum permutation group literature. Our main tool for proving these results is the introduction of orbits and orbitals (orbits on ordered pairs) of quantum permutation groups. We show that the orbitals of a quantum permutation group form a coherent configuration/algebra, a notion from the field of algebraic graph theory. We then prove that the elements of this quantum orbital algebra are exactly the matrices that commute with the magic unitary defining the quantum group. We furthermore show that quantum isomorphic graphs admit an isomorphism of their quantum orbital algebras which maps the adjacency matrix of one graph to that of the other. We hope that this work will encourage new collaborations among the communities of quantum information, quantum groups, and algebraic graph theory. (C) 2020 Elsevier Inc. All rights reserved

Spectroscopic imaging of single atoms within a bulk solid

The ability to localize, identify and measure the electronic environment of individual atoms will provide fundamental insights into many issues in materials science, physics and nanotechnology. We demonstrate, using an aberration-corrected scanning transmission microscope, the spectroscopic imaging of single La atoms inside CaTiO3. Dynamical simulations confirm that the spectroscopic information is spatially confined around the scattering atom. Furthermore we show how the depth of the atom within the crystal may be estimated.Comment: 4 pages and 3 figures. Accepted in Phys.Rev.Let

Direct Imaging of Electron Orbitals with a Scanning Transmission Electron Microscope

Recent studies of secondary electron (SE) emission in scanning transmission electron microscopes suggest that material's properties such as electrical conductivity, connectivity, and work function can be probed with atomic scale resolution using a technique known as secondary electron e-beam-induced current (SEEBIC). Here, we apply the SEEBIC imaging technique to a stacked 2D heterostructure device to reveal the spatially resolved electron orbital ionization cross section of an encapsulated WSe2 layer. We find that the double Se lattice site shows higher emission than the W site, which is at odds with first-principles modelling of ionization of an isolated WSe2 cluster. These results illustrate that atomic level SEEBIC contrast within a single material is possible and that an enhanced understanding of atomic scale SE emission is required to account for the observed contrast. In turn, this suggests that subtle information about interlayer bonding and the effect on electron orbitals can be directly revealed with this technique

L-carnitine fumarate, L-acetyl-carnitine and other components in male infertility: A pilot study of nutraceutics on sperm motility

The aim of this study was to evaluate any possible effect a combination of L-carnitine, fumarate, acetyl-Lcarnitine, fructose, citric acid, selenium, coenzime Q10, vitamin C, zinc, folic acid and vitamin B12 (Proxeed®) on sperm motility in a group of patients with unexplained asthenozoospermia. Thirty two patients received 1 sachet/day of Proxeed® for three months. Sperm parameters were studied before, during and after this treatment. Motility was also studied by the means of a computerized analysis (CASA system). The results of this study indicate that Proxeed® is able to increase sperm motility, both in a quantitative and qualitative manner. We conclude that oral administration of Proxeed® may improve sperm quality, at least in patients with idiopathic asthenozoospermia

Perfect Strategies for Non-Local Games

We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system quotients. We introduce a new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games. We associate a C*-algebra C * (G) to any imitation game G, and show that the existence of perfect quantum commuting (resp. quantum, local) strategies of G can be characterised in terms of properties of this C*algebra. We single out a subclass of imitation games, which we callmirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra

Perfect Strategies for Non-Local Games

We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system quotients. We introduce a new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games. We associate a C*-algebra C∗(G) to any imitation game G, and show that the existence of perfect quantum commuting (resp. quantum, local) strategies of G can be characterised in terms of properties of this C*-algebra. We single out a subclass of imitation games, which we call mirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra

SNP genotyping elucidates the genetic diversity of Magna Graecia grapevine germplasm and its historical origin and dissemination

Background: Magna Graecia is the ancient name for the modern geopolitical region of South Italy extensively populated by Greek colonizers, shown by archeological and historical evidence to be the oldest wine growing region of Italy, crucial for the spread of specialized viticulture around Mediterranean shores. Here, the genetic diversity of Magna Graecia grape germplasm was assessed and its role in grapevine propagation around the Mediterranean basin was underlined. Results: A large collection of grapevines from Magna Graecia was compared with germplasm from Georgia to the Iberian Peninsula using the 18 K SNP array. A high level of genetic diversity of the analyzed germplasm was determined; clustering, structure analysis and DAPC (Discriminant Analysis of Principal Components) highlighted the genetic relationships among genotypes from South Italy and the Eastern Mediterranean (Greece). Gene flow from east (Georgia) to west (Iberian Peninsula) was identified throughout the large number of detected admixed samples. Pedigree analysis showed a complex and well-structured network of first degree relationships, where the cultivars from Magna Graecia were mainly involved. Conclusions: This study provided evidence that Magna Graecia germplasm was shaped by historical events that occurred in the area due to the robust link between South Italian and Greek genotypes, as well as, by the availability of different thermal resources for cultivars growing in such different winegrowing areas. The uniqueness of this ampelographic platform was mainly an outcome of complex natural or human-driven crosses involving elite cultivars